Two-Step Word Problems with All Operations for Grade 3

Master mathematical reasoning: addition, subtraction, multiplication, and division in sequential problem-solving.

Addition and Subtraction Examples
Addition then Subtraction
Example 1
Emma had 15 stickers. Her mom gave her 8 more stickers. Then she gave 6 stickers to her friend. How many stickers does Emma have now?
Problem Type:

Addition followed by subtraction: First increase the amount, then decrease it.

Solution Approach:
  1. Start with the initial amount
  2. Add the amount received
  3. Subtract the amount given away
  4. Calculate the final amount
15
+
8
=
23
-
6
=
17
Step 1: Initial amount

Emma starts with 15 stickers

Step 2: Add the stickers received

Her mom gave her 8 more
So: 15 + 8 = 23 stickers

Step 3: Subtract the stickers given away

Emma gave 6 to her friend
So: 23 - 6 = 17 stickers

Emma has 17 stickers now.
Final Answer:

Emma has 17 stickers remaining.

Key Points:

• Sequential operations: First operation result becomes input for second

• Story order: Perform operations in the order events happen

• Context tracking: Keep track of what each number represents

Subtraction then Addition
Example 2
Tom had 24 marbles. He lost 9 marbles during playtime. Later, he found 7 more marbles. How many marbles does Tom have now?
Problem Type:

Subtraction followed by addition: First decrease the amount, then increase it.

24
-
9
=
15
+
7
=
22
Step 1: Initial amount

Tom starts with 24 marbles

Step 2: Subtract the lost marbles

He lost 9 marbles
So: 24 - 9 = 15 marbles

Step 3: Add the found marbles

He found 7 more marbles
So: 15 + 7 = 22 marbles

Tom has 22 marbles now.
Final Answer:

Tom has 22 marbles remaining.

Key Points:

• Operation sequence: Follow the chronological order of events

• Change identification: "Lost" means subtraction, "found" means addition

• Result chaining: Use each result as input for the next step

Multiplication and Division Examples
Multiplication then Addition
Example 3
A farmer has 4 baskets. Each basket contains 6 apples. Then he picks 8 more apples from the tree. How many apples does he have altogether?
Problem Type:

Multiplication followed by addition: First calculate repeated addition, then add more.

4×6
=
24
+
8
=
32
Step 1: Calculate total in baskets

4 baskets with 6 apples each
So: 4 × 6 = 24 apples

Step 2: Add the picked apples

He picks 8 more apples
So: 24 + 8 = 32 apples

Step 3: State the final answer

The farmer has 32 apples altogether

The farmer has 32 apples.
Final Answer:

The farmer has 32 apples altogether.

Key Points:

• Group recognition: "Each basket contains" indicates multiplication

• Combining totals: Add the grouped amount to the additional amount

• Sequential processing: Complete first operation before second

Subtraction then Division
Example 4
There were 36 students in the gym. 12 students went back to their classrooms. The remaining students were divided equally into 4 groups. How many students are in each group?
Step 1: Calculate remaining students

Started with 36 students
12 went back to classrooms
So: 36 - 12 = 24 students remain

Step 2: Divide remaining students into groups

24 students divided into 4 equal groups
So: 24 ÷ 4 = 6 students per group

Step 3: State the final answer

There are 6 students in each group

36
-
12
=
24
÷
4
=
6
There are 6 students in each group.
Final Answer:

There are 6 students in each group.

Key Points:

• Sequential operations: Complete subtraction before division

• Equal grouping: "Divided equally" indicates division

• Context understanding: Division creates equal parts

Money Problem
Example 5
Sarah had $20. She spent $8 on a book. Then she earned $5 doing chores. How much money does Sarah have now?
Step 1: Calculate money after purchase

Sarah starts with $20
She spends $8 on a book
So: $20 - $8 = $12

Step 2: Calculate money after earning

She has $12, then earns $5
So: $12 + $5 = $17

Step 3: State the final answer

Sarah has $17 now

$20
-
$8
=
$12
+
$5
=
$17
Sarah has $17 now.
Final Answer:

Sarah has $17 now.

Key Points:

• Unit consistency: Keep track of currency units throughout

• Operation recognition: "Spent" means subtraction, "earned" means addition

• Sequential processing: Complete first operation before second

All Operations Guide
Addition (+)
Used when quantities are combined, increased, or added together.
more added total altogether increased by received got
Subtraction (-)
Used when quantities are removed, decreased, or taken away.
less fewer left remaining decreased by gave away spent
Multiplication (×)
Used for equal groups, repeated addition, or scaling.
each per times groups of multiplied by sets of total in all
Division (÷)
Used for sharing equally or finding how many in each group.
divided equally shared among split into how many in each groups per group
Two Step Problem = First Operation + Second Operation
Problem-Solving Formula
📖
Read Carefully
Understand what the problem is asking
📝
Identify Operations
Find keywords that indicate math operations
🔢
Solve Step by Step
Complete one calculation at a time
✅
Check Answer
Make sure your answer makes sense
Detailed Summary: Two-Step Word Problems All Operations
Definition and Core Concepts

Two-step word problems with all operations are mathematical problems that require two separate calculations using any combination of addition, subtraction, multiplication, and division to find the answer. These problems involve reading a story situation, identifying the mathematical operations needed, and performing calculations in the correct order.

Mathematical reasoning: The ability to think logically about mathematical concepts and apply them to solve problems using various operations.

Problem = (Initial Amount ○ Change₁) ○ Change₂
General Formula (○ = any operation)
Key Definitions:

Word problem: A mathematical question presented in narrative form that describes a real-life situation.

Two-step: Requiring two separate calculations to reach the solution, where the result of the first step becomes the input for the second step.

All operations: Problems that may involve addition, subtraction, multiplication, and/or division in any combination.

Mathematical reasoning: The process of using logical thinking to solve mathematical problems.

Four-Phase Problem-Solving Method:
  1. READ: Carefully read the entire problem to understand the situation and identify all numbers and operations needed
  2. PLAN: Identify which operations are needed and the order in which to perform them (considering all four operations)
  3. SOLVE: Execute the calculations step by step, using the result of the first step in the second step
  4. CHECK: Verify that the answer is correct and makes sense in the context of the problem
Tip 1: Circle or underline important numbers and keywords in the problem.
Tip 2: Draw a simple picture to visualize the problem situation.
Tip 3: Write down the first answer before moving to the second step.
Tip 4: Ask yourself: "Does my final answer make sense in the story?"
Common Errors: Forgetting to carry forward the first result, mixing up the order of operations, misreading the question being asked, performing operations in the wrong sequence, or confusing operation keywords.
Success Strategies: Practice identifying keywords for all four operations, work on sequential thinking, master basic arithmetic operations, and develop the habit of checking answers for reasonableness.
Essential Rules to Remember:

• Keyword Identification: "More" typically means addition, "less/left" means subtraction, "each/per" often indicates multiplication, and "shared/divided equally" indicates division.

• Sequential Processing: Always complete the first step before beginning the second step.

• Result Tracking: Keep the first answer readily available to use in the second step.

• Context Awareness: Understand the real-world meaning of each mathematical operation performed.

• Verification: Always check that your final answer makes logical sense within the problem's context.

Questions & Answers

Question: How do I know which operation to do first in a two-step word problem with all operations?

Answer: The order of operations in word problems typically follows the sequence of events in the story:

  • Chronological order: Do the operation that happens first in the story
  • Look for sequence words: Words like "then," "after," "later," or "next" indicate what happens second
  • Follow the story flow: What happens to the starting amount first? That's your first operation
  • Identify operation keywords: Match words to the appropriate operation (addition, subtraction, multiplication, or division)

For example, in "Emma had 15 stickers, got 8 more, then gave 6 away," the story order is: start with 15, add 8, subtract 6. This tells you exactly what to do first!

Question: My child gets confused when division appears in word problems. How can I help them understand division in context?

Answer: Division in word problems often involves sharing or grouping. Help your child understand by focusing on these concepts:

  • Equal sharing: "Divided equally among" or "shared between" means splitting into equal parts
  • Grouping: "How many in each group?" or "split into groups" means dividing into sets
  • Use manipulatives: Use physical objects to demonstrate actual sharing
  • Connect to multiplication: Show that division is the reverse of multiplication

Practice with real-life examples: sharing cookies among friends, putting toys in boxes equally, or dividing a pizza into slices.

Question: Sometimes I see "each" in a problem and I'm not sure if it means multiplication or division. How do I tell the difference?

Answer: Look at how "each" is used in the sentence:

  • Multiplication: "Each container holds 5 items" means multiply to find total items
  • Division: "Items were divided equally among each person" means divide to find per-person amount
  • Context matters: Look at what's happening in the rest of the sentence
  • Think about the result: Are you finding a total (multiply) or a part (divide)?

For example: "4 containers with 5 apples each" = 4 × 5 = 20 apples. But "20 apples divided among 4 people each" = 20 ÷ 4 = 5 apples per person.